Monday, January 31, 2011

My interest has been from a historical position about how such a system while it developed from that ancient perspective, is still not about a "religious perspective" as to what is to be believed by Lee Smolin.

If we think outside of time, we believe these ideas somehow "existed" before we invented them. If we think in time we see no reason to presume that.Lee Smolin

I of course question what is relative by appointments from him as to what can exist "within and out of time." Since this is a foundation approach with which his whole take depends on, his relative relationships as it is relegated toward perspective about the beginning and the end of the universe, is a position with which one cannot ever assume, hence, the value in religious perspective one is suppose to have in relation to their science? I hope I get this right.

The idea that truth is timeless and resides outside the universe was the essence of Plato's philosophy, exemplified in the parable of the slave boy that was meant to argue that discovery is merely remembering. Lee Smolin

So I needed to put this in perspective, so it is understood that the issue here arises "from within" so that all expression without, inside or outside of time become a relative issue about position and stances assumed and cannot be differentiated to such categories as to it significance as being religious.

Among contemporary cosmologists and physicists, proponents of eternal inflation and timeless quantum cosmology are thinking outside of time. Proponents of evolutionary and cyclic cosmological scenarios are thinking in time. If you think in time you worry about time ending at space-time singularities. If you think outside of time this is an ignorable problem because you believe reality is the whole history of the world at once. Lee Smolin

So, I provided some access to "Plato's Dialogues" so as to give you the the ability to discern what is assume by Lee is what is spoken by and through Plato's own words.

What did you gain by reading that you can now say that what is established as "foundations approached" to being realistic, wafts through the scientific community and distinguishes itself according to some category that allows you to believe that it is religious by inherent and that such searches have no basis according too?

Does he say that explicit....only you can say by such association and quotes, can I say then that I point toward that direction in my assumptions as well. I mean you have been given the opportunity so you decide.

My perspective is about that "Cognitive Tool Kit" and how leading to a "point source" is nothing more then the recognition of coming to a "point source" inside you, that is inside time. What I am saying, is that such perfection is the containment of all that has ever existed, or will ever exist, you are connected to in time, so these thoughts about the before and after are not apart from what happens within in any universe, nor can birth and death be considered outside of it.

This recognition is "the measure of" with which one can assume their foundation. That is, how I see Lee's position. All scientist would agree in that such measure is appropriate, yet such thoughts about time and outside of time pertaining to the Cognitive Tool Kit is not part and parcel of a "religious context" that one could say, "eureka!"

Again, it leads to a Point Source. A "point source" inside time that contain vasts potential?

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History

In classical antiquity, the liberal arts denoted the education worthy of a free person (Latin: liber, “free”).[2] Contrary to popular opinion, freeborn girls were as likely to receive formal education as boys, especially during the Roman Empire—unlike the lack-of-education, or purely manual/technical skills, proper to a slave.[3] The "liberal arts" or "liberal pursuits" (Latin liberalia studia) were already so called in formal education during the Roman Empire; for example, Seneca the Younger discusses liberal arts in education from a critical Stoic point of view in Moral Epistle 88.[4] The subjects that would become the standard "Liberal Arts" in Roman and Medieval times already comprised the basic curriculum in the enkuklios paideia or "education in a circle" of late Classical and Hellenistic Greece.

Contents

Origins

These four studies compose the secondary part of the curriculum outlined by Plato in The Republic, and are described in the seventh book of that work.[1] The quadrivium is implicit in early Pythagorean writings and in the De nuptiis of Martianus Capella, although the term was not used until Boethius early in the sixth century.[2] As Proclus wrote:

The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving[3].

Medieval usage

At many medieval universities, this would have been the course leading to the degree of Master of Arts (after the BA). After the MA the student could enter for Bachelor's degrees of the higher faculties (Theology, Medicine or Law). To this day some of the postgraduate degree courses lead to the degree of Bachelor (the B.Phil and B.Litt. degrees are examples in the field of philosophy, and the B.Mus. remains a postgraduate qualification at Oxford and Cambridge universities).

The study was eidetic, approaching the philosophical objectives sought by considering it from each aspect of the quadrivium within the general structure demonstrated by Proclus, namely arithmetic and music on the one hand,[4] and geometry and cosmology on the other.[5]

The subject of music within the quadrivium was originally the classical subject of harmonics, in particular the study of the proportions between the music intervals created by the division of a monochord. A relationship to music as actually practised was not part of this study, but the framework of classical harmonics would substantially influence the content and structure of music theory as practised both in European and Islamic cultures.

Modern usage

In modern applications of the liberal arts as curriculum in colleges or universities, the quadrivium may be considered as the study of number and its relationship to physical space or time: arithmetic was pure number, geometry was number in space, music number in time, and astronomy number in space and time. Morris Kline classifies the four elements of the quadrivium as pure (arithmetic), stationary (geometry), moving (astronomy) and applied (music) number.[6]

Saturday, January 22, 2011

SOCRATES: Then he who does not know may still have true notions of that which he does not know?

MENO: He has.

SOCRATES: And at present these notions have just been stirred up in him, as in a dream; but if he were frequently asked the same questions, in different forms, he would know as well as any one at last?

MENO: I dare say.

SOCRATES: Without any one teaching him he will recover his knowledge for himself, if he is only asked questions?

MENO: Yes.

SOCRATES: And this spontaneous recovery of knowledge in him is recollection?

MENO: True.

SOCRATES: And this knowledge which he now has must he not either have acquired or always possessed?

MENO: Yes.

SOCRATES: But if he always possessed this knowledge he would always have known; or if he has acquired the knowledge he could not have acquired it in this life, unless he has been taught geometry; for he may be made to do the same with all geometry and every other branch of knowledge. Now, has any one ever taught him all this? You must know about him, if, as you say, he was born and bred in your house.

MENO: And I am certain that no one ever did teach him.

SOCRATES: And yet he has the knowledge?

MENO: The fact, Socrates, is undeniable.

SOCRATES: But if he did not acquire the knowledge in this life, then he must have had and learned it at some other time?

One very old and pervasive habit of thought is to imagine that the true answer to whatever question we are wondering about lies out there in some eternal domain of "timeless truths." The aim of re-search is then to "discover" the answer or solution in that already existing timeless domain. For example, physicists often speak as if the final theory of everything already exists in a vast timeless Platonic space of mathematical objects. This is thinking outside of time.

Scientists are thinking in time when we conceive of our task as the invention of genuinely novel ideas to describe newly discovered phenomena, and novel mathematical structures to express them. If we think outside of time, we believe these ideas somehow "existed" before we invented them. If we think in time we see no reason to presume that.

Plato's problem is the term given by Noam Chomsky to the gap between knowledge and experience. It presents the question of how we account for our knowledge when environmental conditions seem to be an insufficient source of information. It is used in linguistics to refer to the "argument from poverty of the stimulus" (APS). In a more general sense, Plato’s Problem refers to the problem of explaining a "lack of input." Solving Plato’s Problem involves explaining the gap between what one knows and the apparent lack of substantive input from experience (the environment). Plato's Problem is most clearly illustrated in the Meno dialogue, in which Socrates demonstrates that an uneducated boy nevertheless understands geometric principles.

Introduction

What is knowledge? What is experience? How do they interact? Is there a correlational, causal, or reciprocal relationship between knowledge and experience? These and other related questions have been at the forefront of investigation by problem solvers, scientists, psychologists, and philosophers for centuries. These questions, but particularly the problem of how experience and knowledge interrelate, have broad theoretical and practical implications for such academic disciplines as epistemology, linguistics, and psychology (specifically the subdiscipline of thinking and problem solving). Gaining a more precise understanding of human knowledge, whether defined as innate, experiential, or both, is an important part of effective problem solving.

Plato was the first philosopher who systematically inquired into issues such as those noted above. He wrote many dialogues, such as Euthyphro and the Apology, but it is from the Meno that the modern instantiation of Plato’s Problem is derived. In the Meno, Plato theorizes about the relationship between knowledge and experience and provides an explanation for how it is possible to know something that one has never been explicitly taught. Plato believed that we possess innate ideas that precede any knowledge that we gain through experience.

As formulated by Noam Chomsky,[1] accounting for this gap between knowledge and experience is "Plato’s Problem." The phrase has a specific linguistic context with regard to language acquisition but can also be used more generally.

Plato (427 B.C. – 347 B.C.)

Plato

Background

Plato was born into an aristocratic Athenian family. When Plato was a young man, Athens was defeated in the Peloponnesian War, a tragedy he attributed to the democracy (Russell). Plato was principally opposed to democracy, as he believed "democracy passes into despotism" [2]. Several of the political calamities of the day led Plato to propose an ideal form of government in his most famous work, The Republic, which still has profound influences on modern Western political philosophy.

Early work

Plato’s early philosophical endeavors involved poetry discussing many ideas, such as the differences between knowledge and opinion, particulars and universals, and God and man. These early dialogues do not utilize conventional notions of reason. Rather, they appeal to the emotions, the allegorical, the spiritual, and the mythological interests of an ancient speculative mind.

Controversy surrounds the early dialogues in how they are to be interpreted. Some claim that Plato was truly trying to discover objective reality through these mystical speculations while others maintain that the dialogues are stories to be interpreted only as parables, allegories, and emotional appeals to religious experience. Regardless, Plato would come to formulate a more rigorous and comprehensive philosophy later in his life, one that reverberates in contemporary Western thought to this day.

Some of Plato’s famous works are Phaedo, the Crito, and, as noted earlier, the Meno. Within these works are found a comprehensive philosophy that addresses epistemology, metaphysics, ethics, aesthetics, theology, and logic. As noted, most of the writing is in the form of dialogues and arguments to pursue answers to difficult questions and concepts. Plato’s teacher and mentor, Socrates, always plays a significant and formative role in these dialogues.

Socrates (470 B.C. - 399 B.C.)

Socrates

Most of Plato’s philosophical ideas were communicated through his beloved teacher Socrates as a presence in the dialogues. Though Socrates never wrote anything himself, it is evident through Plato’s works that Socrates had an incredible ability to explore the most intense analytical discussions. However, for some there is controversy regarding how much historical fact can be derived from Plato’s Socrates (Russell). Some doubt Socrates ever existed. Others are skeptical as to the accuracy of some of Plato’s dialogues but nonetheless maintain that we can learn a substantial amount of historical information about Socrates from the dialogues. Still others take practically everything Plato wrote about Socrates as veridical history. Regardless, it may be safe to say that Plato never meant to record Socrates verbatim and it may plausibly be concluded that his general ideas were communicated in the dialogues.

Socratic method

As delineated in various writings, the meticulousness, articulation, and sophistication with which Socrates spoke supplies an outstanding problem solving technique – the Socratic Method. The Socratic method may be described as follows: it usually involves others with whom Socrates directly engages (not merely pontificating to an audience), it involves a deep philosophical or ethical question to which an answer was sought, and it usually involves Socrates asking questions either to affirm his understanding of others or to seek their understanding.

If someone disagreed with him, Socrates would execute this process in order to bring about his interlocutor’s reluctant admission of inconsistencies and contradictions. Either Socrates would ask his debators questions about their claims that would lead them to admit their fallacy or Socrates would answer questions by posing questions meant to lead the other to answer their own query.

The Socratic Method

Meno

One such dialogue of Plato’s that utilized the Socratic Method was the Meno. The participants were Socrates, Meno, Anytus, and one of Meno’s slave boys. The dialogue begins with Meno asking Socrates whether virtue can be taught. Socrates responds by stating that he does not know the definition of virtue. Meno replies by stating the characteristics of a virtuous man, to which Socrates responds that the characteristics of a virtuous man may be the by-products of virtuousness but they by no means define virtue. Meno is obliged to agree; to wit, he tries to modify his explanation of virtue. Socrates counters each attempt by pointing to inconsistencies and circular arguments.
Meno seems to commit two fallacies when trying to define virtue. He either defines it using some form of the word itself, or he defines it using other words that call for definitions and explanations themselves. Eventually, Meno is lead to confess his shortcomings as he tries to define the enigmatic term (the Socratic Method is the mechanism that brings about this confession). Socrates claims that a definition of virtue must consist of common terms and concepts that are clearly understood by those in the discussion.
A crucial point in the dialogue is when Socrates tells Meno that there is no such thing as teaching, only recollection of knowledge from past lives, or anamnesis. Socrates claims that he can demonstrate this by showing that one of Meno’s servants, a slave boy, knows geometric principles though he is uneducated. Socrates states that he will teach the boy nothing, only ask him questions to assist the process of recollection. Socrates proceeds to ask the slave boy a series of questions about the size and length of lines and squares, using visual diagrams to aid the boy in understanding the questions. The crucial point to this part of the dialogue is that, though the boy has no training, he knows the correct answers to the questions – he intrinsically knows the Pythagorean proposition.

Innate knowledge

Shortly before the demonstration of Pythagoras’ theorem, the dialogue takes an epistemological turn when the interlocutors begin to discuss the fundamental nature of knowledge. The general question asked is how one can claim to know something when one does not even know what knowledge is. Via the Socratic method, it is shown that the answer to the question posed is innateness - one possesses a priori knowledge.

This is derived from Socrates’ belief that one’s soul existed in past lives and knowledge is transferred from those lives to the current one. "These [ideas] were revealed in a former state of existence, and are recovered by reminiscence (anamnesis) or association from sensible things" [3]. The claim is that one does not need to know what knowledge is before gaining knowledge, but rather one has a wealth of knowledge before ever gaining any experience.

Contemporary parallels

There are contemporary contexts that provide input for the various questions posed here: how to account for the gap between experience and knowledge, what are some of the sources of knowledge, or how much knowledge is possessed prior to experience or without conscious awareness. There are many areas in contemporary linguistics and psychological research that have relevance to these epistemological questions. Linguistic analysis has provided some strong evidence for innate cognitive capacities for language and there are many areas of cognitive psychology that yield hard data from investigations into sources of knowledge. In addition, there are some claims in the Meno that have connections to current research on perception and long-term memory (LTM).

Linguistics

Noam Chomsky

Linguistics is the scientific study of language. Chomskian linguistics (an inclusive, though perhaps informal, label for the theories and methodologies of linguistic study spearheaded by Noam Chomsky, meant to encompass his extensive work and influence in the field) includes everything from Chomsky’s earliest work in transformational grammar to more recent work in the Minimalist Program. More exactly, it is the study of the structure of language, or grammar. Chomskian linguistics is defined by a particular theoretical foundation and methodological approach that sets it apart from other linguistic perspectives, such as those described by functional grammar or structuralism (per Leonard Bloomfield) for example. This particular approach to the study of language is also often referred to as Generative linguistics, which is attributed to Chomsky and his early generative grammar work.

Universal grammar

There are several concepts important to the Chomskian (or generativist) approach to linguistics. The most fundamental of these ideas is the theory of universal grammar (UG). Simply put, and as implied by the name, UG refers to those grammatical properties thought to be shared by all (to be universal to all) derivations of human language (anything from Amharic to Zhuang).

Per this conceptualization, UG is innate to all humans – people come "pre-wired" with this universal grammatical structure. A person’s individual grammar (that which is unique to the person) develops from the interaction between the innate universal grammar and input from the environment, or primary linguistic data. This "analytic triplet" (McGilvray, ed., 2005, p. 51), UG + input = grammar, is the functional core of the theory.

Language acquisition

Several questions (or problems) motivate linguistic theorizing and investigation. Two such taken up in Chomskian linguistics are the process of language acquisition in children, and "Plato’s Problem." These subjects are interrelated and viewed as evidence in support of the theory of UG.

One of the simplest ways to approach the concept of universal grammar is to pose a hypothetical question about an aspect of language acquisition in children – why does a child learn the language that it does. As a specific example, how can a child of Asian descent (say, born of Chinese parents) be set down in the middle of Topeka, Kansas and acquire "perfect English?" The answer is that the child does not start with "Chinese," or any other conventionally defined language, in its head. The child does start with general grammatical rules that determine linguistic properties.

Children come equipped with universal grammar, from which any natural human language will develop – without instruction. All that is needed is passive input. If what the child predominantly hears (or sees via sign) as it is maturing through the critical period (in linguistics, that period within which a child must have necessary and sufficient exposure to human language so that language acquisition occurs; without sufficient exposure to primary linguistic data, the UG does not have the necessary input required for the development of an individual grammar; this period is commonly recognized as spanning from birth to adolescence, generally up to 12-years-old, though a shorter or longer critical period is possible on a person-by-person basis) is the English spoken in Topeka, Kansas, then that is what the child will acquire. This is why, regardless of a child’s ethnic/racial background (or any other of a variety of non-relevant factors), the child will know Cockney English, Egyptian Arabic, or isiZulu if the child’s primary linguistic input is Cockney English, Egyptian Arabic, or isiZulu, respectively.

The hypothetical question posed addresses a common misconception about what, exactly, is instantiated in the mind/brain of an individual when it comes to language. It does not address the "logical problem" of language acquisition, i.e., how children transition from ostensibly having no knowledge of language to having full knowledge, in what may be described as a very limited time with apparently limited input.

Plato's problem

To address the issue of apparently limited input, one must turn to what is possibly the most quoted of all arguments in support of universal grammar and its nativist interpretation – Plato’s Problem. The phrase refers to the Socratic dialogue, the Meno; Noam Chomsky is often attributed with coining the term. Plato's Problem particularly refers to a point in the dialogue when Socrates is talking with an uneducated servant and shows, through this interaction, that the servant knows the Pythagorean Theorem though he has never been explicitly taught any geometry. How does the servant know without having ever been taught? Plato’s suggestion is, essentially, that people have innate knowledge.

In the field of linguistics, Plato’s Problem is the problem of finding an explanation for how a child acquires language though the child does not receive explicit instruction and the primary linguistic data (input, or stimuli, from the environment; PLD is necessary for the development of an individual's grammar - language - via input into UG) a child does receive is limited. This limited

Contents

Characters

Plato's Meno is a Socratic dialogue in which the two main speakers, Socrates and Meno, discuss human virtue: whether or not it can be taught, whether it is shared by all human beings, and whether it is one quality or many. As is typical of a Socratic dialogue, there is more than one theme discussed within Meno. One feature of the dialogue is Socrates' use of one of Meno's slaves to demonstrate his idea of anamnesis, that certain knowledge is innate and "recollected" by the soul through proper inquiry. Another often noted feature of the dialogue is the brief appearance of Anytus, a member of a prominent Athenian family who later participated in the prosecution of Socrates.
Meno is visiting Athens with a large entourage of slaves attending him. Young, good-looking and well-born, Meno is perhaps a sophist from Thessaly, but Plato is not absolutely clear about this. Meno says early on in the dialogue that he has held forth many times on the subject of virtue, and in front of large audiences.

Virtue

The dialogue begins with Meno asking Socrates to tell him if virtue can be taught. Socrates says that he is clueless about what virtue is, and so is everyone else he knows (71b). Meno responds that virtue is different for different people, that what is virtuous for a man is to conduct himself in the city so that he helps his friends, injures his enemies, and takes care all the while that he personally comes to no harm. Virtue is different for a woman, he says. Her domain is the management of the household, and she is supposed to obey her husband. He says that children (male and female) have their own proper virtue, and so do old men -free- or slave, as you like (71e). Socrates says he finds this odd. He suspects that there must be some virtue common to all human beings.

Socrates rejects the idea that human virtue depends on a person's gender or age. He leads Meno towards the idea that virtues are common to all people, that temperance ("sophrosunê"- exercising self control) and justice ("dikê, dikaiosunê"- refraining from harming other people) are virtues even in children and old men (73b). Meno proposes to Socrates that the "capacity to govern men" may be a virtue common to all people. Socrates points out to the slaveholder that "governing well" cannot be a virtue of a slave, because then he would not be a slave (73c,d).

One of the errors that Socrates points out is that Meno lists many particular virtues without defining a common feature inherent to virtues which makes them thus. Socrates remarks that Meno makes many out of one, like somebody who breaks a plate (77a).

Meno proposes that virtue is the desire for good things and the power to get them. Socrates points out that this raises a second problem- many people do not recognize evil (77d,e). The discussion then turns to how to account for the fact that so many people are mistaken about good and evil, and take one for the other. Socrates asks Meno to consider whether good things must be acquired virtuously in order to be really good (78b). Socrates leads onto the question of whether virtue is one thing or many.

No satisfactory definition of virtue emerges in the Meno. Socrates' comments however show that he considers a successful definition to be unitary, rather than a list of varieties of virtue, that it must contain all and only those terms which are genuine instances of virtue, and must not be circular.[1]

Meno eventually throws up his hands at the problem, confessing that he is no longer so sure of what virtue is. He seems agitated and compares Socrates to a torpedo fish that can numb, and admits that he is "quite perplexed". He says that Socrates has made him numb in his mind and tongue (80a,b). Socrates argues that the reason for this comparison is that Meno, a "handsome" man, is inviting counter-comparisons because of his own vanity. Socrates tells Meno that he only resembles a stingray if it numbs itself in making others numb (80c).

Meno's paradox

Socrates brings Meno to aporia (puzzlement) on the question of what virtue is. Meno responds by accusing Socrates of being like a 'torpedo fish' (meaning some species of electric ray), which stuns its victims. Meno then proffers a paradox, "And how will you inquire into a thing when you are wholly ignorant of what it is? Even if you happen to bump right into it, how will you know it is the thing you didn't know?" (80d1-4). This paradox has troubled philosophers for generations.

Meno asks Socrates how a person can look for something when he has no idea what it is. How can he know when he has arrived at the truth when he does not already know what the truth is?(80d) Socrates avoids this sophistical paradox by pointing out that, by using this logic, man could neither search for what he does know, because he would already know it, nor for what he does not know, because he would not know for what he was looking. (This is not to say that Socrates or Plato deny the strength of this paradox. Socrates does not take the position that knowledge can be sought; as is explained, his theory of knowledge is that it is never acquired, only ever recollected.)

Plato subsequently discusses his own theory of knowledge through Socrates, that it is "recollection" from the past lives of the immortal soul.(81d)

Dialogue with Meno's slave

The blue square is twice the area of the original yellow square

Socrates does not answer the paradox. Instead he counters with a mythos (poetic story): the theory of recollection. It tells of our immortal souls mixing with the objects of knowledge in a great world-spirit. Since we have contact with real things in this stage of existence prior to birth, we have only to 'recollect' them when alive. Such recollection requires Socratic questioning, which according to Plato is not 'teaching.' Socrates thus demonstrates his method of questioning and recollection by interrogating a slave who is ignorant of geometry. The subsequent discussion shows the slave capable of learning a complex geometry problem, because "he already has the questions in his soul." In this way, Socrates shows Meno that learning is possible through recollection, and that the paradox is false. Meno's aporia shows that he is not capable of learning, but the examination of the slave shows that he can learn. In this way, Socrates answers Meno's paradox with one of his own. Not understanding, Meno attempts to avoid Socrates' ironic criticism by returning to his original question: "what is virtue?"
Socrates begins one of the most influential dialogues of Western philosophy regarding the argument for innate knowledge. By drawing geometric figures in the ground Socrates demonstrates that the slave is initially unaware of how to find twice the area of a square.
Socrates then said that before he got hold of him the slave (who has been picked at random from Meno's entourage) has spoken "well and fluently" on the subject of a square double the size of a given square (84c). Socrates comments that this "numbing" he caused in the slave did him no harm (84b).

Socrates then draws a second square figure on the diagonal so that the slave can see that by adding vertical and horizontal lines touching the corners of the square, the double of its area is created. He gets the slave to agree that this is twice the size of the original square and says that he has "spontaneously recovered" knowledge he knew from a past life (85d) without having been taught. Socrates is satisfied that new beliefs were "newly aroused" in the slave.
After witnessing the example with the slave boy, Meno tells Socrates that he thinks that Socrates is correct in his theory of recollection, to which Socrates replies, “I think I am. I shouldn’t like to take my oath on the whole story, but one thing I am ready to fight for as long as I can, in word and act—that is, that we shall be better, braver, and more active men if we believe it right to look for what we don’t know...” (86b). It has been argued variously that this implies Socrates is skeptical regarding knowledge or that he is a pragmatist. It also prepares us for the subsequent discussion of knowledge by hypothesis.

Anytus

When Anytus appears, Socrates praises him as the son of Anthemion, who earned his fortune with intelligence and hard work. He says that Anthemion had his son well-educated, and Anytus, the beneficiary of a well-meaning father, must both be virtuous and know what it is. Anytus comments on Sophists, and saying that he neither knows any, nor cares to know any. Socrates then questions why it is that men do not always produce sons of the same virtue as themselves. He alludes to other notable male figures, such as Themistocles, Aristides, Pericles and Thucydides, and casts doubt on whether these men produced sons as capable of virtue as themselves. Anytus becomes offended and accuses Socrates of slander, warning him to be careful expressing such opinions. (The historical Anytus was one of Socrates' accusers in his trial.)

After speaking to Anytus, Socrates suggests that Anytus does not realize what slander is, and continues his dialogue with Meno as to the definition of Virtue.

Concluding dialogue with Meno

After the discussion with Anytus, Socrates and Meno return to the subject of whether Virtue can be taught. Socrates points out the similarities and differences between "true beliefs" and "knowledge". He claims that while "true beliefs" may be as useful to us as knowledge, they often fail to "stay in their place" and must be "tethered" by what he calls aitias logismos (the calculation of reason, or reasoned explanation), immediately adding that this is anamnesis, or recollection.[2] Whether or not Plato intends that the tethering of true beliefs with reasoned explanations must always involve anamnesis is explored in later interpretations of the text.[3][4] Socrates' distinction between "true beliefs" and "knowledge" forms the basis of the philosophical definition of knowledge as "justified true belief". Myles Burnyeat and others, however, have argued that the phrase aitias logismos refers to a practical working out of a solution, rather than a justification.[5]

"To sum up our enquiry," Socrates concludes, "the result seems to be, if we are at all right in our view, that virtue is neither natural nor acquired, but an instinct given by God to the virtuous." In most modern readings these closing remarks are "evidently ironic",[6] but Socrates' invocation of the gods may be sincere, albeit "highly tentative".[7]

Meno and Protagoras

Meno's theme is also being dealt in the dialogue of Protagoras, where, Plato finally puts Socrates to conclude with the opposite conclusion 'That virtue can be taught.' And, whereas in the Protagoras knowledge is uncompromisingly this-worldly, in the Meno the theory of recollection points to a link between knowledge and eternal truths.[8]